Mike Bolsinger starts Wednesday night against the Athletics.
Kershaw didn't want to discuss whether the soreness was related to the hip impingement that sidelined him briefly in 2012, causing a couple starts to be pushed back.
"It's a little sore right now," Kershaw said multiple times, not delving much deeper into his current state.
Manager Don Mattingly said Kershaw didn't feel anything in his last start, on Thursday in New York, a three-hit shutout of the Mets. But Kershaw felt soreness in his hip during his bullpen session, and the soreness remained on Tuesday.
"I thought he would really be ready to roll tonight, but yesterday he wasn't that great," Mattingly said. "At that point, we have [Bolsinger] ready, the off day coming. We just want to take advantage of the off day.
"Yesterday he was still a little tender. Once I saw his face coming in, I knew. We had already thought about this."
The Dodgers were off Monday, and they have off days again on Thursday and next Monday. The current plan is for Kershaw to start on Friday against the Angels, with Zack Greinke starting Saturday on five days rest.
If Kershaw is healthy, that is.
"If he's not 100 percent Friday, we won't start him," Mattingly said.